Sample Paper - 2008 Class X Subject Mathematics

Sample Paper - 2008
Class – X
Subject – Mathematics

Time: 3 hrs M.M: 80

SECTION – A(10 * 1=10)

1.Write the condition to be satisfied by q so that a rational number has a terminating decimal expansion.

2.State Euclid’s division lemma.

3.Probability of a sure event is ______and impossible event is ______.

4.The sum and product of the zeroes of a quadratic polynomial are and –3 respectively. What is the quadratic polynomial.

5.Find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:

9x + 3y + 12 = 0, 18x + 6y + 24 = 0

6.Which term of the sequence 114, 109, 104.. is the first negative term?

7.Prove that if the areas of two similar triangles are equal, they are congruent.

8.If perimeter & area of a circle are numerically equal then diameter of circle is ______

9.In Fig., if TP and TQ are the two tangents to a circle with centre O so that POQ = 110 °, then PTQ is

10.The wickets taken by a bowler in 10 cricket matches are as follows:

2, 6, 4, 5, 0, 2, 1, 3,2,3

Find the median of the data.

SECTION B(5 * 2=10)

11.Using Euclid’s division algorithm, find the HCF of 56, 96, and 404.

12.On throwing two dice together what is the probability of getting sum 7 , difference 5.

13.The distance between A (1, 3) and B(x, 7) is 5. Find the possible values of x

14.Prove that

With out using trigonometric tables, evaluate the following: .

15.If 3 cot A = 4, check whether = cos2 A — sin2 A or not

SECTION C((10 * 3=30)

16.Prove that is irrational.

17.Ais a point on the y-axis whose ordinate is 5 and B is the point (-3, 1). Calculate the length of AB.

18.Find the value of p for which the following system of equations has no solution
(3p + 1)x + 3y – 2 =0; (p2 + 1)x + (p – 2)y – 5 = 0.

19.Draw the graph of x-y+1=0 and 3x+2y-12=0 calculate the area bounded by these lines and x-axis.

20.How many numbers between 20 and 200 are exactly divisible by 7. Find their sum.

21.Find equation of perpendicular bisector of A ( 3 , 6 ) & B ( -3 , 4 ).

22.A girl of height 90 cm is walking away from the base of a lamp-post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.

23.Four equal circles each of radius 7 cm touch each other externally .Find of region included between them.

24.Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

25. BL and CM are medians of triangle ABC right angled at A .Prove that 4(BL2 + CM2 ) = 5 BC2

SECTION D(5 * 6=30)

26.A person on tour has Rs. 360 For his daily expenses. If he exceeds his tour programme by 4 days, he must cut down his daily expenses by Rs. 3 per day. Find the number of days of his tour programme.

A two-digit number is such that the product of the digits is 6. When 9 is subtracted from the number the digits interchange their position. Determine the number.

27.If the angle of elevation of a cloud from a point ‘h’ meters high above the lake is α and angle of depression of its reflection in the lake is β ,prove that height of cloud is

28.Prove that The lengths of tangents drawn from an external point to a circle are equal. PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length TP.

29. Water in a canal, 6m wide and 1.5m deep, is flowing with a speed of 10km/hr. How much area will it irrigatein 30 minutes, if 8cm standing water is needed?

30.The following distribution gives the daily income of 50 workers of a factory.Convert the distribution above to a less than type and more than type cumulative frequency distributions, draw its ogives and hence find the median.

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